There are 6 people in a room. If everyone shakes everyone else's hand exactly once, how many handshakes occur?
Solution: Given 6 people, each person shakes the hands of 5 other people. The following is almost the answer. $6 \times 5 = 30$ We have double counted the handshakes though, since William shaking Ashley's hand is the same handshake as Ashley shaking William's hand. Therefore, the following is the correct answer. $\dfrac{6 \times 5}{2} = 15$